Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Pascal's Law01:04

Pascal's Law

12.5K
In 1653, the French philosopher and scientist Blaise Pascal published "Treatise on the Equilibrium of Liquids," which discussed the principles of static fluids. A static fluid is a fluid that is not in motion. When a fluid is not flowing, we say that the fluid is in static equilibrium. If the fluid is water, we say it is in hydrostatic equilibrium. For a fluid in static equilibrium, the net force on any part of the fluid must be zero; otherwise, the fluid will start to flow. Pascal...
12.5K
Newton's Law of Gravitational Attraction01:24

Newton's Law of Gravitational Attraction

1.9K
Sir Isaac Newton established the universality of the law of gravitational attraction based on empirical evidence and inductive reasoning. He published his work in Philosophiae Naturalis Principia Mathematica ("the Principia") on July 5, 1687.
Newton's law of gravitational attraction is a fundamental law of physics that governs the attraction between objects. It states that the magnitude of the gravitational force between any two objects is proportional to their masses and inversely...
1.9K
First Law: Particles in One-dimensional Equilibrium01:10

First Law: Particles in One-dimensional Equilibrium

8.6K
Newton's first law of motion states that a body at rest remains at rest, or if in motion, remains in motion at constant velocity, unless acted on by a net external force. It also states that there must be a cause for any change in velocity (a change in either magnitude or direction) to occur. This cause is a net external force. For example, consider what happens to an object sliding along a rough horizontal surface. The object quickly grinds to a halt, due to the net force of friction. If...
8.6K
Introduction to Limits01:30

Introduction to Limits

405
A limit describes the value a function approaches as its input moves closer to a particular point. Even when a function is undefined at a specific value, limits allow us to analyze its behavior near that point. This concept is fundamental in calculus and essential for understanding continuity, derivatives, and integrals.Mathematically, a function f(x) has a limit L at x = a if its values L approach x as x gets arbitrarily close to a. This is written as:This notation expresses that the function...
405
Limit Laws II01:26

Limit Laws II

335
In calculus, limit laws serve as foundational tools for evaluating the behavior of functions as inputs approach specific values. Among these, the laws concerning quotients, powers, and roots are particularly useful in breaking down complex expressions.The Quotient Law allows the limit of a division between two functions to be calculated by dividing their individual limits, provided the limit of the denominator exists and is not zero. For example,The Power Law states that the limit of a function...
335
Probability Laws01:49

Probability Laws

45.4K
Overview
45.4K

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Flecainide-Induced Interstitial Lung Disease: A Case Report and Review of the Literature.

Clinical case reports·2026
Same author

Regularized Multilevel Multinomial Regression for Select-All-That-Apply Responses and High-Dimensional Predictors with Applications to Perception of Facial Expressions.

Psychometrika·2026
Same author

Design principles for topological thermoelectrics.

Reports on progress in physics. Physical Society (Great Britain)·2026
Same author

Chiral Wigner Crystal Phases Induced by Berry Curvature.

Physical review letters·2026
Same author

A Picture is Worth a Thousand Clinical Assessments: Use of Video-Based Pose Estimation to Augment Post-Stroke Upper Limb Assessment of Bilateral Tasks.

Restorative neurology and neuroscience·2025
Same author

Dynamic Facial Health Predicts Psychological First Impressions with Applications to Tailored Treatments for Facial Paralysis.

Journal of personalized medicine·2025

Related Experiment Video

Updated: Apr 19, 2026

Simulation of Human-induced Vibrations Based on the Characterized In-field Pedestrian Behavior
10:52

Simulation of Human-induced Vibrations Based on the Characterized In-field Pedestrian Behavior

Published on: April 13, 2016

9.3K

Universal power law governing pedestrian interactions.

Ioannis Karamouzas1, Brian Skinner2, Stephen J Guy1

  • 1Department of Computer Science and Engineering, University of Minnesota, Minneapolis, Minnesota 55455, USA.

Physical Review Letters
|December 20, 2014
PubMed
Summary

Researchers developed a new statistical-mechanical method to measure pedestrian interaction energy. This method reveals a predictive collision-based interaction law governing human crowd dynamics across various scenarios.

More Related Videos

Using a Virtual Reality Walking Simulator to Investigate Pedestrian Behavior
06:38

Using a Virtual Reality Walking Simulator to Investigate Pedestrian Behavior

Published on: June 9, 2020

5.4K
Trajectory Data Analyses for Pedestrian Space-time Activity Study
16:14

Trajectory Data Analyses for Pedestrian Space-time Activity Study

Published on: February 25, 2013

14.3K

Related Experiment Videos

Last Updated: Apr 19, 2026

Simulation of Human-induced Vibrations Based on the Characterized In-field Pedestrian Behavior
10:52

Simulation of Human-induced Vibrations Based on the Characterized In-field Pedestrian Behavior

Published on: April 13, 2016

9.3K
Using a Virtual Reality Walking Simulator to Investigate Pedestrian Behavior
06:38

Using a Virtual Reality Walking Simulator to Investigate Pedestrian Behavior

Published on: June 9, 2020

5.4K
Trajectory Data Analyses for Pedestrian Space-time Activity Study
16:14

Trajectory Data Analyses for Pedestrian Space-time Activity Study

Published on: February 25, 2013

14.3K

Area of Science:

  • Complex Systems
  • Statistical Mechanics
  • Human Dynamics

Background:

  • Human crowds are often modeled as interacting particle systems.
  • Previous models used physical separation for interaction forces, but the quantitative form remained unclear.
  • Understanding pedestrian interaction is crucial for crowd management and safety.

Purpose of the Study:

  • To introduce a novel statistical-mechanical approach for measuring pedestrian interaction energy.
  • To identify the fundamental quantitative law governing pedestrian interactions.
  • To validate the identified law's ability to reproduce known crowd phenomena.

Main Methods:

  • Developed a statistical-mechanical framework to directly quantify interaction energy between pedestrians.
  • Applied the framework to a large dataset of human motion data.
  • Conducted simulations to test the sufficiency of the identified interaction law.

Main Results:

  • Discovered a simple power-law interaction governing pedestrian behavior.
  • The interaction is based on projected time to potential collision, not physical distance, indicating an anticipatory nature.
  • This law accurately describes interactions across diverse situations, speeds, and densities.

Conclusions:

  • The identified anticipatory, collision-time-based interaction law provides a fundamental description of pedestrian dynamics.
  • This simple law is sufficient to reproduce complex crowd behaviors observed in simulations.
  • The findings offer a new quantitative basis for understanding and modeling human crowds.